scholarly journals Clique minors in graphs with a forbidden subgraph

2021 ◽  
Author(s):  
Matija Bucić ◽  
Jacob Fox ◽  
Benny Sudakov
Keyword(s):  
Forbidden Subgraph

scholarly journals Toughness, Forbidden Subgraphs and Pancyclicity

2021 ◽  
Vol 37 (3) ◽  
pp. 839-866
Author(s):  
Wei Zheng ◽  
Hajo Broersma ◽  
Ligong Wang
Keyword(s):  
Recent Article ◽  
Forbidden Subgraph ◽  
Forbidden Subgraphs ◽  
Free Graph ◽  
Induced Subgraph ◽  
Complete Answer ◽  
Open Case

AbstractMotivated by several conjectures due to Nikoghosyan, in a recent article due to Li et al., the aim was to characterize all possible graphs H such that every 1-tough H-free graph is hamiltonian. The almost complete answer was given there by the conclusion that every proper induced subgraph H of $$K_1\cup P_4$$ K 1 ∪ P 4 can act as a forbidden subgraph to ensure that every 1-tough H-free graph is hamiltonian, and that there is no other forbidden subgraph with this property, except possibly for the graph $$K_1\cup P_4$$ K 1 ∪ P 4 itself. The hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs, as conjectured by Nikoghosyan, was left there as an open case. In this paper, we consider the stronger property of pancyclicity under the same condition. We find that the results are completely analogous to the hamiltonian case: every graph H such that any 1-tough H-free graph is hamiltonian also ensures that every 1-tough H-free graph is pancyclic, except for a few specific classes of graphs. Moreover, there is no other forbidden subgraph having this property. With respect to the open case for hamiltonicity of 1-tough $$K_1\cup P_4$$ K 1 ∪ P 4 -free graphs we give infinite families of graphs that are not pancyclic.

scholarly journals Matrix Partitions with Finitely Many Obstructions

10.37236/976 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Tomás Feder ◽  
Pavol Hell ◽  
Wing Xie
Keyword(s):  
Symmetric Matrix ◽  
Forbidden Subgraph ◽  
Input Graph ◽  
Induced Subgraphs ◽  
Induced Subgraph ◽  
Forbidden Induced Subgraphs ◽  
Extra Effort ◽  
Matrix Partition ◽  
Finite Set ◽  
Forbidden Induced Subgraph

Each $m$ by $m$ symmetric matrix $M$ over $0, 1, *$, defines a partition problem, in which an input graph $G$ is to be partitioned into $m$ parts with adjacencies governed by $M$, in the sense that two distinct vertices in (possibly equal) parts $i$ and $j$ are adjacent if $M(i,j)=1$, and nonadjacent if $M(i,j)=0$. (The entry $*$ implies no restriction.) We ask which matrix partition problems admit a characterization by a finite set of forbidden induced subgraphs. We prove that matrices containing a certain two by two diagonal submatrix $S$ never have such characterizations. We then develop a recursive technique that allows us (with some extra effort) to verify that matrices without $S$ of size five or less always have a finite forbidden induced subgraph characterization. However, we exhibit a six by six matrix without $S$ which cannot be characterized by finitely many induced subgraphs. We also explore the connection between finite forbidden subgraph characterizations and related questions on the descriptive and computational complexity of matrix partition problems.

scholarly journals Automated generation of conjectures on forbidden subgraph characterization

2014 ◽  
Vol 162 ◽  
pp. 177-194
Author(s):  
Christian Desrosiers ◽  
Philippe Galinier ◽  
Pierre Hansen ◽  
Alain Hertz
Keyword(s):  
Forbidden Subgraph ◽  
Automated Generation ◽  
Forbidden Subgraph Characterization

scholarly journals Universal graphs with a forbidden subgraph: Block path solidity

COMBINATORICA ◽  
2015 ◽  
Vol 36 (3) ◽  
pp. 249-264 ◽  
Author(s):  
Gregory Cherlin ◽  
Saharon Shelah
Keyword(s):  
Forbidden Subgraph ◽  
Universal Graphs

scholarly journals Forbidden subgraph decomposition

2002 ◽  
Vol 247 (1-3) ◽  
pp. 159-168 ◽  
Author(s):  
Irena Rusu ◽  
Jeremy Spinrad
Keyword(s):  
Forbidden Subgraph

scholarly journals On minimal forbidden subgraph characterizations of balanced graphs

2009 ◽  
Vol 35 ◽  
pp. 41-46 ◽  
Author(s):  
Flavia Bonomo ◽  
Guillermo Durán ◽  
Martín D. Safe ◽  
Annegret K. Wagler
Keyword(s):  
Forbidden Subgraph ◽  
Balanced Graphs

Forbidden subgraph and perfect path-matchings

2009 ◽  
Author(s):  
Jingzhi Yan ◽  
Bin Hu ◽  
Heping Zhang ◽  
Tingzhao Zhu ◽  
Xiaowei Li
Keyword(s):  
Forbidden Subgraph

scholarly journals The complexity of forbidden subgraph sandwich problems and the skew partition sandwich problem

2015 ◽  
Vol 182 ◽  
pp. 15-24 ◽  
Author(s):  
Simone Dantas ◽  
Celina M.H. de Figueiredo ◽  
Frédéric Maffray ◽  
Rafael B. Teixeira
Keyword(s):  
Forbidden Subgraph
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